Was Lucy REALLY the cold-as-ice brains behind the show?

I'm hardly an expert on the history of I Love Lucy, so perhaps I'm mistaken here. But I never got the impression she was the main force behind so many of the creative and business decisions. Is this incorrect? Or is this movie really over-aggrandizing her in regards to these things?

It seems to paint the picture almost as if she's some sort of comedy savant. Cold, calculating, deeply analytical, and all business. It shows her imagining brilliant comedy to life as if she's John Nash dreaming up explanations to the universe in A Beautiful Mind (it even plays A Beautiful Mind-esque music when we see her fantasizing how these skits will play out). We see her hauling Vivian Vance and William Frawley into the studio in the middle of the night to go Stanley Kubrick on them. Having them repeat takes and really sharpening scenes to perfection. Is this actually something that occurred? Because I'd never heard about this before.

From the interviews I've heard from Lucy, she speaks as if she's never had particularly good instincts for comedy. In fact, she's mentioned how she was just good at acting out, verbatim, what was written on the page for her by other people (including gestures). To my knowledge, she never wrote or directed any episodes herself. She wasn't coming up with the bits herself. And, going by Lucy's own comments, it seems like Desi Arnaz was far more active in the business aspects than she was (I seem to recall her even putting it as: "He built an empire").

Also, as far as how cold and Devil Wears Prada-like she's seen in the movie (that's how she came off to me, at least), from the footage I've seen of her (from interviews, game shows, and award shows, primarily), this doesn't appear to be anything like her in reality. She seemed very humble and down-to-earth any time I'd seen her. And, despite her claims, she does appear naturally funny, kinda silly, cute, sweet, and charismatic in conversation. The Lucy in this film, however, looks to have a stick permanently up her ass, with the charm and personality of an accountant.

Again, I've not done any in-depth research on this matter (I've read no bios or anything) so maybe I'm way off here and this depiction is closer to reality than I'm thinking. But my knee-jerk reaction is that this is a highly inaccurate take on her as a person.